14.1 Earth Satellites
An earth satellite is a projectile that falls around the earth rather than into it.
If a projectile, such as a satellite, is falling at precisely the right speed, it will then fall into an orbit.
Imagine yourself on a planet much smaller than the earth. If you throw a stone from your planet at the right speed. The speed that one must throw the stone for it to land itself into an orbit depends on the rate at which the stone falls and the rate at which the earth curves.
The earths surface drops a vertical distance of 5m for every 8000 meters tangent to the surface.
not to scale
A stone that would be thrown fast enough to go a horizontal distance of 8 kilometers during the time (one second) it takes to fall five meters will follow the curvature of the earth. The speed that this stone would be thrown is 8 kilometers per second. The orbital speed for close orbit around the earth is 8 km/s or 29000 km/h.
14.2 Circular Motion
Gravity has no effect on the speed of a circling satellite in a circular orbit. This is because the gravity only has a vertical effect not a horizontal effect. In the direction of the orbit, the satellite is always moving perpendicular to the force of gravity. Therefore the satelites are always moving at a constant speed.
The period, or the time it takes to complete one orbit, for a satellite close to the earth is about 90 minutes. Satellites that are further away from the earth have a longer period. The moon, for example, has a 27.3 day period.
14.3 Elliptical Orbits
A projectile shot at a horizontal speed more than 8 km/s will go farther than into a circular path. It will fall into an ellipse, or an oval shaped path.
Satallite speed is constant when in circular orbit, but it is not in an elliptical orbit. Because the projectile overshoots the 8 km/s, it is farther away from the earth. It is then moving against the force of gravity that reduces its speed
The projectile, after being shot into the air will slowly lose speed as it gets farther away from the earth. It will then stop loosing speed at the top and begin to regain is speed at on the way back down.
14.4 Energy Conservation and Satellite Motion
While a satellite is in motion, it has a constant Kinetic energy and potential energy. Because the distance between a planets center and the satellites center is constant while in circular orbit, the PE (potential energy) and the KE (kinetic energy) is also constant. This is due to the law of conservation of energy.
The situation is different while in an elliptical orbit. This is because the speed and the distance from the earth varies as the satellite moves around the orbit.
The PE is the greatest when the projectile is the farthest away from the earth (this is known as the apogee) . It is the least when the satellite is the closest (or the perigee). It is the opposite for the KE. Due to the constant balance of the KE and PE, the sum of these amounts is constant.
There is a component of gravitation force that is parallel to the direction of satellite motion at all points on the orbit except the apogee and perigee. The component of gravitation changes the speed of the projectile.
(the component of force) x (distance moved) = the change in KE.
The satellite's KE and speed decreases as the satellite against altitude and moves against the component. It continues to decrease as it moves in the direction of the apogee and then moves in the same direction as the component. This creates the speed and the KE to increase. Then the cycle continues.
14.5 Escape Speed
Neglecting air resistance, anything shot at a speed greater than 11.2 km/s will leave the earth. It will gradually reduce speed but it will never stop.
Close to the earth, the force of gravity is very strong. Therefore, he work done on launching a vertical projectile (a rocket) is done mostly near the earth. The value of PE for a 1-kilogram at a distance of infinity is 62 million joules (MJ). a payload such as a rocket needs at leats 62 MJ of energy per kilogram of load. This corresponds to a speed of 11.2 km/s or the value of the escape speed.
If a projectile is launched in a vertical motion at a greater speed than the escape speed, neglecting air resistance, will escape from the earth. It wll never return because the PE will increase and the KE will decrease. the speed will decrease but it is never reduced to zero. Therefore, it will eventually leave the relm of the earths gravity and it escapes forever.
There are different ecape speeds for different astronomical bodys.
Chapter 14 - Satellite Motion
14.1 Earth Satellites
An earth satellite is a projectile that falls around the earth rather than into it.
If a projectile, such as a satellite, is falling at precisely the right speed, it will then fall into an orbit.
Imagine yourself on a planet much smaller than the earth. If you throw a stone from your planet at the right speed. The speed that one must throw the stone for it to land itself into an orbit depends on the rate at which the stone falls and the rate at which the earth curves.
The earths surface drops a vertical distance of 5m for every 8000 meters tangent to the surface.
A stone that would be thrown fast enough to go a horizontal distance of 8 kilometers during the time (one second) it takes to fall five meters will follow the curvature of the earth. The speed that this stone would be thrown is 8 kilometers per second. The orbital speed for close orbit around the earth is 8 km/s or 29000 km/h.
14.2 Circular Motion
Gravity has no effect on the speed of a circling satellite in a circular orbit. This is because the gravity only has a vertical effect not a horizontal effect. In the direction of the orbit, the satellite is always moving perpendicular to the force of gravity. Therefore the satelites are always moving at a constant speed.
The period, or the time it takes to complete one orbit, for a satellite close to the earth is about 90 minutes. Satellites that are further away from the earth have a longer period. The moon, for example, has a 27.3 day period.
14.3 Elliptical Orbits
A projectile shot at a horizontal speed more than 8 km/s will go farther than into a circular path. It will fall into an ellipse, or an oval shaped path.
Satallite speed is constant when in circular orbit, but it is not in an elliptical orbit. Because the projectile overshoots the 8 km/s, it is farther away from the earth. It is then moving against the force of gravity that reduces its speed
The projectile, after being shot into the air will slowly lose speed as it gets farther away from the earth. It will then stop loosing speed at the top and begin to regain is speed at on the way back down.
14.4 Energy Conservation and Satellite Motion
While a satellite is in motion, it has a constant Kinetic energy and potential energy. Because the distance between a planets center and the satellites center is constant while in circular orbit, the PE (potential energy) and the KE (kinetic energy) is also constant. This is due to the law of conservation of energy.
The situation is different while in an elliptical orbit. This is because the speed and the distance from the earth varies as the satellite moves around the orbit.
The PE is the greatest when the projectile is the farthest away from the earth (this is known as the apogee) . It is the least when the satellite is the closest (or the perigee). It is the opposite for the KE. Due to the constant balance of the KE and PE, the sum of these amounts is constant.
There is a component of gravitation force that is parallel to the direction of satellite motion at all points on the orbit except the apogee and perigee. The component of gravitation changes the speed of the projectile.
(the component of force) x (distance moved) = the change in KE.
The satellite's KE and speed decreases as the satellite against altitude and moves against the component. It continues to decrease as it moves in the direction of the apogee and then moves in the same direction as the component. This creates the speed and the KE to increase. Then the cycle continues.
14.5 Escape Speed
Neglecting air resistance, anything shot at a speed greater than 11.2 km/s will leave the earth. It will gradually reduce speed but it will never stop.
Close to the earth, the force of gravity is very strong. Therefore, he work done on launching a vertical projectile (a rocket) is done mostly near the earth. The value of PE for a 1-kilogram at a distance of infinity is 62 million joules (MJ). a payload such as a rocket needs at leats 62 MJ of energy per kilogram of load. This corresponds to a speed of 11.2 km/s or the value of the escape speed.
If a projectile is launched in a vertical motion at a greater speed than the escape speed, neglecting air resistance, will escape from the earth. It wll never return because the PE will increase and the KE will decrease. the speed will decrease but it is never reduced to zero. Therefore, it will eventually leave the relm of the earths gravity and it escapes forever.
There are different ecape speeds for different astronomical bodys.